Скачать или смотреть Finding Eigenvalues and Eigenvectors with `numpy.linalg.eig()`

Eigenvalues and eigenvectors are critical concepts in linear algebra, used extensively in fields like data science, physics, and engineering. Eigenvalues are scalars, and eigenvectors are vectors associated with a square matrix. They are used to understand the properties of the matrix, such as its behavior under transformation. NumPy provides the `numpy.linalg.eig()` function to compute the eigenvalues and eigenvectors of a matrix. This function returns a tuple with the first element being an array of eigenvalues and the second element being an array of the corresponding eigenvectors. Understanding how to compute and interpret these values is crucial for tasks like Principal Component Analysis (PCA), which is widely used for dimensionality reduction in machine learning. We'll walk through an example to see how `numpy.linalg.eig()` can be applied in real-world data analysis tasks.